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We discuss a concept of loopoid as a non-associative generalization of Brandt groupoid. We introduce and study also an interesting class of more general objects which we call semiloopoids. A differential version of loopoids is intended as a framework for Lagrangian discrete mechanics.

An obstruction to represent abelian Lie algebras by unipotent matrices.

J. C. Benjumea, F. J. Echarte, Núñez, J.,Tenorio, A. F. (2004)

Extracta Mathematicae

The aim of this paper is the study of abelian Lie algebras as subalgebras of the nilpotent Lie algebra gn associated with Lie groups of upper-triangular square matrices whose main diagonal is formed by 1. We also give an obstruction to obtain the abelian Lie algebra of dimension one unit less than the corresponding to gn as a Lie subalgebra of gn. Moreover, we give a procedure to obtain abelian Lie subalgebras of gn up to the dimension which we think it is the maximum.

Another representation for the maximal Lie algebra of $𝔰𝔩 (n + 2, ℝ)$ in terms of operators.

Feroze, Tooba, Qadir, Asghar (2009)

Differential Equations & Nonlinear Mechanics

Applications of the characteristic identity for GL(N)

M. D. Gould (1978)

Annales de l'I.H.P. Physique théorique

Approximation in Lie transformation groups by superposition of one-parameter subgroups. (Approximation in Lieschen Transformationsgruppen durch Überlagerung von einparametrigen Untergruppen.)

Wallner, Johannes (1995)

Mathematica Pannonica

Bounded bicircular domains in Cn.

Dimitris-Panayotis Panou (1990)

Manuscripta mathematica

Champs de vecteurs adjoints sur les groupes et algèbres de Lie semi-simples.

J. Dixmier (1979)

Journal für die reine und angewandte Mathematik

Classification of 4-Dimensional Generalized Symmetric Planes.

Hans-Peter Seidel (1991)

Forum mathematicum

Classification of the irreducible representations of the groups $I O (n)$

Fritz Schwarz (1971)

Annales de l'I.H.P. Physique théorique

Comments on a paper of Brown and Guivarc'h : “Espaces de Poisson des groupes de Lie”

Calvin C. Moore, Jonathan Rosenberg (1975)

Annales scientifiques de l'École Normale Supérieure

Contraction semigroups and representations.

Karl-Hermann Neeb (1994)

Forum mathematicum

Control Systems on the Orthogonal Group SO(4)

Ross M. Adams, Rory Biggs, Claudiu C. Remsing (2013)

Communications in Mathematics

We classify the left-invariant control affine systems evolving on the orthogonal group $S O (4)$ . The equivalence relation under consideration is detached feedback equivalence. Each possible number of inputs is considered; both the homogeneous and inhomogeneous systems are covered. A complete list of class representatives is identified and controllability of each representative system is determined.

Convolution des courants sur un groupe de Lie

Marianne Guillemot-Teissier (1962)

Annales scientifiques de l'École Normale Supérieure

Correction to the paper "The structure space of the trigonometric polynomials on a comapct group".

Kelly McKennon (1984)

Journal für die reine und angewandte Mathematik

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